Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Figures
Thumbnails
page
|<
<
of 355
>
>|
<
archimedes
>
<
text
>
<
body
>
<
chap
>
<
p
type
="
main
">
<
s
id
="
s.000729
">
<
pb
pagenum
="
37
"
xlink:href
="
009/01/037.jpg
"/>
bus vltimis, non prætereundum. </
s
>
<
s
id
="
s.000730
">reliquas duas logicæ partes, Topicam ſci
<
lb
/>
licet, & Elenchos, quæ ſyllogiſmos probabilem, & apparentem docent, no
<
lb
/>
luit appellare reſolutorios, quamuis inuentionem mediorum doceant, quia
<
lb
/>
iam mos iſte inoleuerat apud Philoſophos, & Mathematicos, vt illa ſola
<
lb
/>
pars, quæ ex materia neceſſaria doceret ſyllogiſmum demonſtratiuum con
<
lb
/>
ſtruere, diceretur reſolutio: cum Mathematici, qui primi de reſolutione
<
lb
/>
ſcripſerunt, talem materiam ſolum conſiderent.</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000731
">
<
arrow.to.target
n
="
marg5
"/>
</
s
>
</
p
>
<
p
type
="
margin
">
<
s
id
="
s.000732
">
<
margin.target
id
="
marg5
"/>
5</
s
>
</
p
>
<
p
type
="
main
">
<
s
id
="
s.000733
">Ex cap. 23. ſecti primi lib. 1.
<
emph
type
="
italics
"/>
(Vt quod diameter incommenſurabilis eo, quod
<
lb
/>
imparia æqualia paribus fiant, ſi fuerit poſita commenſurabilis. </
s
>
<
s
id
="
s.000734
">æqualia igitur fieri
<
lb
/>
imparia paribus ratiocinantur, diametrum vtrò incommenſurabilem eſſe ex ſuppo
<
lb
/>
ſitione
<
expan
abbr
="
monſtrãt
">monſtrant</
expan
>
, quoniam falſum accidit propter contradictionem)
<
emph.end
type
="
italics
"/>
Euclides pri
<
lb
/>
mis duabus definitionibus 10. elem. </
s
>
<
s
id
="
s.000735
">definit, quæ nam ſint magnitudines
<
lb
/>
commenſ. </
s
>
<
s
id
="
s.000736
">& quæ incommenſ. </
s
>
<
s
id
="
s.000737
">ſic; commenſ. </
s
>
<
s
id
="
s.000738
">magnitudines dicuntur, quas
<
lb
/>
<
figure
id
="
id.009.01.037.1.jpg
"
place
="
text
"
xlink:href
="
009/01/037/1.jpg
"
number
="
3
"/>
<
lb
/>
eadem menſura metitur, vt ſi fuerint duæ magnitu
<
lb
/>
dines, A, & B, quas eadem menſura C, ideſt quan
<
lb
/>
titas C, metiatur, ideſt
<
expan
abbr
="
quãtitas
">quantitas</
expan
>
C, applicata quan
<
lb
/>
titati A, & per ipſam aliquoties replicata ipſam ad
<
lb
/>
æquatè abſumat, vt ſi linea C, quinquies ſuper li
<
lb
/>
neam A, replicata eam præcisè, & perfectè omninò
<
lb
/>
adæquaret: & eadem linea C, applicata lineæ B, & ſuper illam ter, v.g. re
<
lb
/>
petita ipſam conſumeret, diceretur
<
expan
abbr
="
vtranq;
">vtranque</
expan
>
metiri, & proinde duas lineas
<
lb
/>
A, & B, eſſe comm. definit poſtea
<
expan
abbr
="
incommẽſ
">incommenſ.</
expan
>
hoc modo, incomm. autem, qua
<
lb
/>
rum nullam contingit communem menſuram reperiri; vt ſi duarum linea
<
lb
/>
<
figure
id
="
id.009.01.037.2.jpg
"
place
="
text
"
xlink:href
="
009/01/037/2.jpg
"
number
="
4
"/>
<
lb
/>
rum, A, B, nunquam poſſet reperiri aliqua menſu
<
lb
/>
ra, quæ
<
expan
abbr
="
vtranq;
">vtranque</
expan
>
adæquatè metiretur, v. g. ſi linea
<
lb
/>
C, menſuraret A, quater ſumpta, ter autem ſumpta
<
lb
/>
non adæquaret omnino
<
expan
abbr
="
lineã
">lineam</
expan
>
B, ſed deficeret, vel ex
<
lb
/>
cederet aliquantulum,
<
expan
abbr
="
atq;
">atque</
expan
>
hoc fieret in quauis alia
<
lb
/>
menſura, loco ipſius C, aſſumpta, ſiue maior, ſiue
<
lb
/>
minor ipſa C, vt
<
expan
abbr
="
vtranq;
">vtranque</
expan
>
nunquam perfectè metiretur, eſſent duæ illæ lineæ
<
lb
/>
incommenſ. </
s
>
<
s
id
="
s.000739
">Extare porrò tales lineas, & ſuperficies, & corpora,
<
expan
abbr
="
eaq́
">eaque</
expan
>
; quam
<
lb
/>
plurima, ac penè infinita ex 10. Elem. manifeſtum eſt. </
s
>
<
s
id
="
s.000740
">inuentum autem hu
<
lb
/>
ius aſymmetriæ, quod Pythagoricis veteres attribuunt, mihi ſemper viſum
<
lb
/>
eſt omni maius admiratione, cum nulla experientia,
<
expan
abbr
="
nullusq́
">nullusque</
expan
>
; effectus in ip
<
lb
/>
ſius cognitionem potuerit priſcos illos Geometras inducere. </
s
>
<
s
id
="
s.000741
">Quapropter
<
lb
/>
non immeritò diuinus ille Plato lib. 7. de legib. </
s
>
<
s
id
="
s.000742
">huius aſymmetriæ ignora
<
lb
/>
tionem, adeo deteſtatus eſt, vt eam non hominum, ſed ſuum, pecorumque
<
lb
/>
ignorantiam cenſuerit. </
s
>
<
s
id
="
s.000743
">inter lineas incommenſ. ſunt diameter, & latus eiuſ
<
lb
/>
dem quadrati, quia nulla poteſt reperiri menſura quantumuis exigua, vti
<
lb
/>
<
figure
id
="
id.009.01.037.3.jpg
"
place
="
text
"
xlink:href
="
009/01/037/3.jpg
"
number
="
5
"/>
<
lb
/>
eſt lineola E, in præſenti quadrato, etiamſi illam in
<
lb
/>
infinitum ſubdiuidas, quæ
<
expan
abbr
="
vtranq;
">vtranque</
expan
>
lineam, diame
<
lb
/>
trum ſcilicet A C, & latus quoduis ex quatuor, v.g.
<
lb
/>
latus B C, præcisè omnino metiatur. </
s
>
<
s
id
="
s.000744
">theorema
<
lb
/>
iſtud demonſtratur in vltima 10. Elem. eodem me
<
lb
/>
dio, quod ab Ariſtotele hic innuitur; Euclides ex
<
lb
/>
ſuppoſitione alterius partis contradictionis ipſius </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>